There are around 160 different ethnic groups indigenous to what is now defined as Russia. Tatars are just under 4% of the population at just over 5 million residents.
The following lists all ethnicities resolved by the 2010 census, grouped by language:
Indo-European 116,443,421 (84.86%)
Slavic 113,545,521 (82.74%)
East Slavs 113,466,552 (82.68%)
Russians 111,016,896 (80.90%)
Ukrainians 1,927,988 (1.40%)
Belarusians 521,443 (0.38%)
Ruthenians 225 (0.00%)
West Slavs 49,347 (0.03%)
Poles 47,125 (0.03%)
Czechs 1,898 (0.00%)
Slovaks 324 (0.00%)
South Slavs 29,622 (0.02%)
Bulgarians 24,038 (0.02%)
Serbs 3,510 (0.00%)
Slovenes 1,008 (0.00%)
Macedonians 325 (0.00%)
Croats 304 (0.00%)
Bosnians 256 (0.00%)
Montenegrins 181 (0.00%)
Armenian 1,184,435 (0.86%)
Armenians 1,182,388 (0.86%)
Hemshins 2,047 (0.00%)
Hellenic 856,640 (0.6%)
Pontic Greeks (including Caucasus Greeks)
Iranic 806,953 (0.59%)
Ossetians 528,515 (0.39%)
Tajiks 200,303 (0.15%)
Yazidis 40,586 (0.03%)
Kurds 23,232 (0.02%)
Afghans 5,350 (0.00%)
Persians 3,696 (0.00%)
Talysh 2,529 (0.00%)
Tats 1,585 (0.00%)
Pamiris 363 (0.00%)
Germanic 396,660 (0.29%)
Germans 394,138 (0.29%)
Indo-Aryan 209,572 (0.15%)
Roma 204,958 (0.15%)
Indians 4,058 (0.00%)
Pakistani 507 (0.00%)
Central Asian Gypsies 49 (0.00%)
Baltic 50,356 (0.04%)
Lithuanians 31,377 (0.02%)
Latvians 18,979 (0.01%)
Romance 164,284 (0.12%)
Moldovans 156,400 (0.11%)
Romanians 3,201 (0.00%)
French 1,475 (0.00%)
Italians 1,370 (0.00%)
Spanish 1,162 (0.00%)
Cubans 676 (0.00%)
other
Americans 1,572 (0.00%)
British 950 (0.00%)
Mountain Jews 762 (0.00%)
Central Asian Jews 32 (0.00%)
Turkic 12,006,361 (8.75%)
Northwestern Turkic (Kipchak) 8,596,762 (6.26%)
Volga Tatars 5,310,649 (3.87%)
Bashkirs 1,584,554 (1.15%)
Kazakhs 647,732 (0.47%)
Kumyks 503,060 (0.37%)
Karachays 218,403 (0.16%)
Balkars 112,924 (0.08%)
Nogais 103,660 (0.08%)
Kyrgyz 103,422 (0.08%)
Nağaybäk 8,148 (0.01%)
Crimean Tatars 2,449 (0.00%)
Karakalpaks 1,466 (0.00%)
Karaites 205 (0.00%)
Krymchaks 90 (0.00%)
Oghur 1,435,872 (1.05%)
Chuvashs 1,435,872 (1.05%)
Northeastern Turkic (Siberian) 916,641 (0.67%)
Yakuts 478,085 (0.35%)
Tuvans 263,934 (0.19%)
Altay 74,238 (0.05%)
Khakas 72,959 (0.05%)
Shors 12,888 (0.01%)
Dolgans 7,885 (0.01%)
Kumandins 2,892 (0.00%)
Teleuts 2,643 (0.00%)
Tofalars 762 (0.00%)
Chulyms 355 (0.00%)
Southwestern Turkic (Oghuz) 763,528 (0.56%)
Azerbaijani 603,070 (0.44%)
Turks 105,058 (0.08%)
Turkmens 36,885 (0.03%)
Gagauz 13,690 (0.01%)
Meskhetian Turks 4,825 (0.00%)
Southeastern Turkic (Karluk) 293,558 (0.21%)
Uzbeks 289,862 (0.21%)
Uyghurs 3,696 (0.00%)
Mongolic 651,355 (0.47%)
Buryats 461,389 (0.34%)
Kalmyks 183,372 (0.13%)
Soyots 3,608 (0.00%)
Khalkha Mongols 2,986 (0.00%)
Caucasian 5,194,015 (3.78%)
Northeast Caucasian 4,262,817 (3.11%)
Chechens 1,431,360 (1.04%)
Avars 912,090 (0.66%)
Dargins 589,386 (0.43%)
Lezgins 473,722 (0.35%)
Ingush 444,833 (0.32%)
Laks 178,630 (0.13%)
Tabasarans 146,360 (0.11%)
Rutuls 35,240 (0.03%)
Aguls 34,160 (0.02%)
Tsakhurs 12,769 (0.01%)
Udis 4,267 (0.00%)
Northwest Caucasian 773,317 (0.56%)
Kabardians 516,826 (0.38%)
Adyghe 124,835 (0.09%)
Cherkess 73,184 (0.05%)
Abazas 43,341 (0.03%)
Abkhaz 11,249 (0.01%)
Shapsugs 3,882 (0.00%)
Kartvelian 157,881 (0.12%)
Georgians 157,803 (0.11%)
Georgian Jews 78 (0.00%)
Uralic 2,371,398 (1.73%)
Permic 877,191 (0.64%)
Udmurts 552,299 (0.40%)
Komi 228,235 (0.17%)
Komi-Permyak 94,456 (0.07%)
Besermyan 2,201 (0.00%)
Mordvins 744,237 (0.54%)
Mari 547,605 (0.40%)
Baltic Finnic 105,223 (0.06%)
Karelians 60,815 (0.04%)
Finns 20,267 (0.01%)
Estonians 17,875 (0.01%)
Veps 5,936 (0.00%)
Izhorians 266 (0.00%)
Votes 64 (0.00%)
Samoyedic 49,378 (0.04%)
Nenets 44,640 (0.03%)
Selkups 3,649 (0.00%)
Nganasans 862 (0.00%)
Enets 227 (0.00%)
Khanty 30,943 (0.02%)
Mansi 12,269 (0.01%)
Hungarians 2,781 (0.00%)
Sami 1,771 (0.00%)
Just off the top of my head, of course